Almost all studies of the densest particle packings consider convex particles. Here, we provide exact constructions for the densest known two-dimensional packings of superdisks whose shapes are defined by $|x_1{|}^{2p}+|x_2{|}^{2p}\le 1$ and thus contain a large family of both convex ($p\ge 0.5$) and concave ($0<p<0.5$) particles. Our candidate maximal packing arrangements are achieved by certain families of Bravais lattice packings, and the maximal density is nonanalytic at the “circular-disk” point ($p=1$) and increases dramatically as $p$ moves away from unity. Moreover, we show that the broken rotational symmetry of superdisks influences the packing characteristics in a nontrivial way.

• Received 23 February 2008

DOI:https://doi.org/10.1103/PhysRevLett.100.245504